I agree with you on many of your points. Yes, the exponential growth rate is only a component of the question. As you also pointed out, extinction rates, ecological niches, birth rates, major disasters, and other factors must be included.
And yes, as I fully expect that human influence to open up new ecological niches that animals will evolve into. Rats in the city are a prime example.
My post wasn't really aimed at you, I just hit reply and forgot to put Ahban on the list, but I'm glad you agree :)